IDAKLUSolver

The IDAKLUSolver is the recommended solver for most PyBaMM simulations. It uses the SUNDIALS IDA integrator with the KLU sparse direct linear solver, and supports parallelism, Hermite interpolation, and output-variable selection.

pybamm.IDAKLUSolver is generally the fastest solver for lithium-ion battery models. It wraps the SUNDIALS IDA DAE integrator with the KLU sparse-direct linear solver, provided by the pybammsolvers package.

Constructor

pybamm.IDAKLUSolver(
    rtol=1e-4,
    atol=1e-6,
    root_method="casadi",
    root_tol=1e-6,
    extrap_tol=None,
    on_extrapolation=None,
    on_failure="error",
    output_variables=None,
    options=None,
)

rtol · float · default: "1e-4"

Relative tolerance for the IDA integrator.

atol · float · default: "1e-6"

Absolute tolerance for the IDA integrator.

root_method · str · default: "\"casadi\""

Method for consistent initial conditions. "casadi" uses CasADi’s Newton solver; any scipy.optimize.root method string is also accepted.

root_tol · float · default: "1e-6"

Tolerance for the root-finding step.

extrap_tol · float | None · default: "0"

Tolerance for detecting extrapolation beyond the solved interval.

on_extrapolation · str · default: "\"warn\""

Behaviour on extrapolation: "warn", "error", or "ignore".

on_failure · str · default: "\"error\""

Behaviour when the solver returns an error flag: "error", "warn", or "ignore".

output_variables · list[str] | None · default: "[]"

If provided, only these variables are computed during the solve. This can significantly reduce memory usage and solve time for large models.

options · dict | None · default: "{}"

Advanced solver options. See the Options reference below.

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Options Reference

The options dict exposes the full SUNDIALS IDA configuration. All keys and their defaults:

Key	Default	Description
print_stats	False	Print solver statistics after each solve
num_threads	1	Number of OpenMP threads
num_solvers	num_threads	Number of parallel solvers (for input-parameter sweeps)
linear_solver	"SUNLinSol_KLU"	SUNDIALS linear solver. Options: "SUNLinSol_KLU", "SUNLinSol_Dense", "SUNLinSol_Band", "SUNLinSol_SPBCGS", "SUNLinSol_SPGMR", etc.
jacobian	"sparse"	Jacobian form: "none", "dense", "banded", "sparse", "matrix-free"
preconditioner	"BBDP"	Preconditioner for iterative solvers: "none" or "BBDP"
max_order_bdf	5	Maximum order of the BDF linear multistep method
max_num_steps	100000	Maximum steps to reach the next output time
dt_init	0.0	Initial step size (0 = solver chooses)
dt_min	0.0	Minimum absolute step size (0 = solver chooses)
dt_max	0.0	Maximum absolute step size (0 = solver chooses)
max_error_test_failures	10	Maximum error-test failures per step
max_nonlinear_iterations	40	Maximum nonlinear iterations per step
max_convergence_failures	100	Maximum nonlinear convergence failures per step
hermite_interpolation	True	Store Hermite interpolation data. Disabled when output_variables are given.
hermite_reduction_factor	1.0	Compression factor for Hermite spline (values > 1 reduce storage with a small accuracy cost)
suppress_algebraic_error	False	Exclude algebraic variables from the error test
silence_sundials_errors	False	Suppress SUNDIALS error messages during solve
calc_ic	True	Calculate consistent initial conditions
init_all_y_ic	False	If True, compute all y₀ given ẏ₀; if False, compute algebraic y₀ and differential ẏ₀ given differential y₀

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Examples

Default usage

import pybamm

solver = pybamm.IDAKLUSolver()

sim = pybamm.Simulation(
    pybamm.lithium_ion.DFN(),
    parameter_values=pybamm.ParameterValues("Chen2020"),
    solver=solver,
)
sol = sim.solve([0, 3600])
print(sol["Terminal voltage [V]"].entries[-1])

IDAKLUSolver is the default solver used by pybamm.Simulation when no solver is specified. For most lithium-ion simulations, the defaults are a good starting point.